install.packages("tidyverse")
install.packages("knitr")
install.packages("fitdistrplus")

library(tidyverse)
library(fitdistrplus)

# Options: 
# data <- read_csv("path/to/where/you/downloaded/it")
# navigate to the file in your file explorer pane. Click on the file and "import dataset"
data <- read_csv("https://tinyurl.com/sim-bag-data")
head(data)

data |> ggplot(aes(x = Arrival)) +
  geom_histogram(binwidth=60*60*3, color = "black") +
  labs(
    title = "Histogram of Plane Arrival Times",
    x = "Arrival Time",
    y = "Count of Planes? Bags? What?"
  ) +
  theme_minimal()

# set timezones so the datetime will DISPLAY correctly
data <- data |> mutate(
          Arrival = as.POSIXct(Arrival, tz = "EST")) |>
        mutate(
          bag_completion_time = as.POSIXct(bag_completion_time,
          tz = "EST"))

kable(head(data))

flight_arrivals <- data |>
  distinct(`Flight Number`, Arrival)

ggplot(flight_arrivals, aes(x = Arrival)) +
  geom_histogram(binwidth=60*60*3, fill = "lightblue", color = "black") + # Binwidth = 1 hour (3600 seconds)
  labs(
    title = "Histogram of Plane Arrival Times",
    x = "Arrival Time",
    y = "Count of Planes"
  ) +
  theme_dark()

data <- data |> mutate(bag_delivery_time = as.numeric(bag_completion_time - Arrival))

data |> ggplot(aes(x = bag_delivery_time)) + 
  geom_histogram()

x_bar <- mean(data$bag_delivery_time)
s <- sd(data$bag_delivery_time)

summary(data)

f_norm <- fitdist(data$bag_delivery_time, "norm")
f_ln <- fitdist(data$bag_delivery_time, "lnorm")
f_weibull <- fitdist(data$bag_delivery_time, "weibull")
f_gamma <- fitdist(data$bag_delivery_time, "gamma")

plot.legend <- c("Normal", "LogNormal", "Weibull", "Gamma")

denscomp(
  list(f_norm, f_ln, f_weibull, f_gamma),
  xlab = "Bag Delivery Time (min)",
  legendtext = plot.legend)

data <- data |> mutate(
  Weibull = dweibull(bag_delivery_time,
                      shape = f_weibull$estimate["shape"],
                      scale = f_weibull$estimate["scale"]),
  Normal = dnorm(bag_delivery_time,
                      mean = f_norm$estimate["mean"],
                      sd = f_norm$estimate["sd"]),
  Gamma = dgamma(bag_delivery_time,
                      shape = f_gamma$estimate["shape"],
                      rate = f_gamma$estimate["rate"]),
  LogNormal = dlnorm(bag_delivery_time,
                      meanlog = f_ln$estimate["meanlog"],
                      sdlog = f_ln$estimate["sdlog"]),
)

data |> ggplot(aes(x = bag_delivery_time)) +
  geom_line(aes(y = Gamma, color="Gamma", line="grey")) +
  geom_line(aes(y = Normal, color="Normal")) +
  geom_line(aes(y = LogNormal, color="LogNormal")) +
  labs(
    color = "Distribution",
    x = "Bag Delivery Time (min)",
    y = "Probability Density"
  )

long_data <- data |> pivot_longer(
  cols = c(Gamma, LogNormal, Normal, Weibull),
  names_to = "Distribution",
  values_to = "Probability")

kable(head(long_data))

ggplot() +
  # Histogram or density plot of `bag_delivery_time`
  geom_histogram(data = data, aes(x = bag_delivery_time, y = ..density..), 
                 bins = 30, color="black", fill = "skyblue", alpha = 0.5) +
  # Overlay probability density lines from `long_data`
  geom_line(data = long_data, aes(x = bag_delivery_time, y = Probability, color = Distribution), size=1)

fitted_distributins <- list(f_gamma, f_ln, f_norm, f_weibull)

# Extract summary metrics from the fitted distributions
summary_table <- sapply(fitted_distributins, function(fit) {
  c(
    "Number of Parameters" = as.integer(length(fit$estimate)),  # Number of parameters
    "Log-Likelihood" = fit$loglik,                # Log-likelihood
    "AIC" = fit$aic,                              # Akaike Information Criterion
    "BIC" = fit$bic                               # Bayesian Information Criterion
  )
})

# Convert to a data frame for readability
# summary_table <- as.data.frame(summary_table)

# Assign column names based on your distributions
colnames(summary_table) <- c("Gamma", "Log-Normal", "Normal", "Weibull")  # Adjust based on distribution names

# View the table
#kable(summary_table)